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HI Stefan,
If you mean to have 3.3V out the output of the device, then absolutely the TPS709 can remain connected. The TPS709 is unique in that it has true reverse current protection meaning if at anytime, the VOUT is higher than VIN, the device will prevent current flowing in the reverse direction.
As for UVLO, this question does come up and this UVLO on this IC is simply not well defined. As long and the IC is above or equal to 2.7V at VIN, it is guaranteed to work.
I hope this answers your question.
7.3.2 Dropout Voltage
The TPS709 use a PMOS pass transistor to achieve low dropout voltage.
When (VIN – VOUT) is less than the dropout voltage (VDO),
the PMOS pass device is in the linear region of operation and the input-to-output resistance is the RDS(ON) of the PMOS pass element.
VDO approximately scales with the output current because the PMOS device functions like a resistor in dropout.
HI Stefan,
Yes. with VIn at 3.3V the TPS709833 will do its best to try to regulate 3.3Vout. so it will basically be working as a load switch at this point. The actual output voltage will be VIN-VDO*ILOAD.
Does this make sense?
Regards,